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MAT540/MAT 540 FINAL EXAM VERSION 3
MAT 540
FINAL EXAM III
The following sales data are available for 2003-2008 :
Year Sales Forecast
2003 7 9
2004 12 10
2005 14 15
2006 20 22
2007 16 18
2008 25 21
Calculate the MAPD and express it in decimal notation. Please express the result as a number with 4 decimal places. If necessary, round your result accordingly. For instance, 9.14677, should be expressed as 9.1468
Ford- Bed & Breakfast breaks even if they sell 50 rooms each month. They have a fixed cost of $6500 per month. The variable cost per room is $30. For this model to work, what must be the revenue per room? (Note: The answer is a whole dollar amount. Give the answer as a whole number, omitting the decimal point. For instance, use 105 to write $105.00).
Answer
Joseph is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. What is the probability that Jim will not be accepted at either university? (Note: write your answer as a probability, with two decimal places. If necessary, round to two decimal places. For instance, a probability of 0.252 should be written as 0.25).
Students are organizing a "Battle of the Bands" contest. They know that at least 100 people will attend. The rental fee for the hall is $200 and the winning band will receive $500. In order to guarantee that they break even, how much should they charge for each ticket? (Note: Write your answer with two significant places after the decimal and do not include the dollar “$†sign. For instance, for five dollars, write your answer as 5.00).
In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?
Answer
The Kirschner Company has a contract to produce garden hoses for a customer. Kirschner has 5 different machines that can produce this kind of hose. Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.
Answer
Find the optimal Z value for the following problem. Do not include the dollar “$†sign with your answer.
Kalamazoo Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality of care the pets receive, including well balanced nutrition. The kennel- cat food is made by mixing two types of cat food to obtain the “nutritionally balanced cat diet.†The data for the two cat foods are as follows:
Cat Food Cost/oz protien (%) fat (%)
Pet's Choice 0.35 40 15
Feline Chow 0.32 20 30
Kalamazoo Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3 ounces of fat per day. What is the optimal cost of this plan? Note: Please write your answers with two significant places after the decimal and do not include the dollar “$†sign. For instance, $9.45 (nine dollars and fortyfive cents) should be written as 9.45
Consider the following decision tree. The objective is to choose the best decision among the two available decisions A and B. Find the expected value of the best decision. Do not include the dollar “$†sign with your answer.
Let us take as a given that x is normally distributed with a mean of 8.5 and a standard deviation of 2, what is P(x ≤ 6)? Note: Round your answer, if necessary, to two places after the decimal. Please express your answer with two places after the decimal.
Answer
Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.
Formulation:
Let x = number of tractors produced per period
y = number of lawn mowers produced per period
MAX 30x + 30y
subject to 2 x + y ≤ 60
2 x + 3y ≤ 120
x ≤ 45
x, y ≥ 0
The graphical solution is shown below.
What is the shadow price for assembly? Write your answers with two significant places after the decimal and do not include the dollar “$†sign.
Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.
Formulation:
Let x = number of tractors produced per period
y = number of lawn mowers produced per period
MAX 30x + 30y
subject to 2 x + y ≤ 60
2 x + 3y ≤ 120
x ≤ 45
x, y ≥ 0
The graphical solution is shown below.
What is the shadow price for fabrication? Write your answers with two significant places after the decimal and do not include the dollar “$†sign.
In linear programming problems, multiple optimal solutions occur
Answer
Using the maximin criterion to make a decision, you
The probability of observing x
successes in a fixed number of trials is a problem related to
Answer
Events that cannot occur at the same time in any trial of an experiment are:
A business owner is trying to decide whether to buy, rent, or lease office space and has constructed the following payoff table based on whether business is brisk or slow.
Given the following linear programming problem that minimizes cost.
Min Z = 2x + 8y
Subject to 8x + 4y ≥ 64
2x + 4y ≥ 32
y ≥ 2
The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What is the optimal weekly profit?
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What are the expected net revenues for the number of workers he will decide to hire? The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.
The local operations manager for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues will vary with how well taxpayers comply with the new tax code. The probabilities of low, medium, and high compliance are 0.20, 0.30, and 0.50 respectively. What is the expected value of perfect information? Do not include the dollar “$†sign with your answer. The following payoff table is given in thousands of dollars (e.g. 50 = $50,000). Note: Please express your answer as a whole number in thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole number, if necessary.
5 out of 5 points
In the Monte Carlo process, values for a random variable are generated by __________ a probability distribution.
Answer
__________ moving averages react more slowly to recent demand changes than do __________ moving averages.
For the following frequency distribution of demand, the random number 0.8177 would be interpreted as a demand of:
5 out of 5 points
Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
Answer
Consider the following network representation of shipment routes between plants, a distribution center, and retail outlets. The numbers next to the arcs represent shipping costs. For example, the cost of shipping from plant 1 to distribution center 3 is equal to 2.
Assume that Plant 1 can supply 400 units and Plant 2, 500 units. Demand at the retail outlets are: Outlet 4, 300 units; Outlet 5, 250 units; Outlet 6, 450 units. Supply is less than demand, so this is an unbalanced transshipment model. Which constraint represents the quantity shipped to retail outlet 6?
Answer
5 out of 5 points
A professor needs help from 3 student helpers to complete 4 tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.
Which of the following constraints represents the assignment for student A?
Answer
5 out of 5 points
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demands for gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.
Answer
The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively. Five essential ingredients are contained in the feed, shown in the table below. The table also shows the minimum daily requirements of each ingredient.
Ingredient Percent per pound in Feed A Percent per pound in Feed B Minimum daily requirement (pounds)
1 20 24 30
2 30 10 50
3 0 30 20
4 24 15 60
5 10 20 40
The constraint for ingredient 3 is:
The metropolitan airport commission is considering the establishment of limitations on noise pollution around a local airport. At the present time, the noise level per jet takeoff in one neighborhood near the airport is approximately normally distributed with a mean of 100 decibels and a standard deviation of 3 decibels. What is the probability that a randomly selected jet will generate a noise level of more than 105 decibels? Note: please provide your answer to 2 places past the decimal point, rounding as appropriate.
Jack is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 30% for University X and 60% for University Y. The decisions of each university have no effect on each other. This means that they are:
Answer
Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the storage space constraint?
Steinmetz furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $100 and requires 100 cubic feet of storage space, and each medium shelf costs $50 and requires 80 cubic feet of storage space. The company has $25000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $85 and for each medium shelf is $75. What is the objective function?
r. Sartre is considering four different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below.
Investment Economic Conditions
Poor
(S1) Average
(S2) Good
(S3) Excellent
(S4)
A 38 25 33 10
B 10 15 20 85
C 20 100 20 -25
D 25 25 100 25
Suppose all states of the world are equally likely (each state has a probability of 0.25). What is the expected value of perfect information? Note: Report your answer as an integer, rounding to the nearest integer, if applicable
5 out of 5 points
Fractional relationships between variables are not permitted in the standard form of a linear program.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
5 out of 5 points
In a transshipment problem, items may be transported from destination to destination and from source to source.
Answer
5 out of 5 points
In an unbalanced transportation model, supply does not equal demand and one set of constraints uses ≤ signs.
Answer
Adjusted exponential smoothing is an exponential smoothing forecast adjusted for seasonality
If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a conditional constraint.
A cycle is an up and down movement in demand that repeats itself in less than 1 year.
Answered
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15 Dec 2015
Answers (1)
MAT540/MAT 540 FINAL EXAM VERSION 3
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